Download Magnetic Properties of Solids

Magnetic Properties of Solids
Magnetic Properties
Magnetic (with unpaired electron)
Materials
Non-magnetic or diamagnetic (electrons all
paired up)
Paramagnetic
Ferromagnetic
Antiferromagnetic
Ferrimagnetic
Magnetic Behavior
B = μH
B = μ0H + μ0M
Induction generated
Induction generated
by the field
by the sample
χ = M/H
χ: magnetic susceptibility
B = μ0H + μ0Hχ
B = μ0H (1 + χ) = μH
μ0 (1 + χ) = μ
(1 + χ) = μ / μ0 = μr
μr: relative permittivity
B: magnetic flux density
μ: permittivity (m0: free space)
H: magnetic field
M: Magnetization
Behavior of Substances in a Magnetic Field
Magnetic behavior may be distinguished by the values of χ and μ
and by their temperature and field dependence
1. Positive vs. negative value: only diamagnetic materials show
negative χ
2. Absolute value: ferromagnetic materials show huge positive value
3. Temperature dependence: diamagnetism is not temp. dependence,
antiferromagentic materials increase with increasing temp, and
para- and ferromagnetic materials decrease with increasing temp
4. Field dependence: only ferro- and antiferromagnetic materials show
field dependence
Effect of Temperature
Paramagnetic substance: obey Curie Law
C: Curie constant
T: temperature
There is no spontaneous interaction between adjacent unpaired electrons.
With increasing temperature the alignment is more difficult and χ decreases.
Paramagnetic substance show some magnetic ordering (ferro- or antiferro):
Curie-Weiss Law
χ=
C
Τ-θ
θ: Weiss constant
There is some spontaneous interaction between adjacent spins. A better fit
to the high temperature behavior in the paramagnetic region is provided by
Curie-Weiss Law (with additional Weiss constant).
Effect of Temperature
Paramagnetic: Curie law; T decrease,
c increase (alignment easier)
Robert John Lancashire (wwwchem.uwimona.edu.jm)
Tc: ferromagnetic Curie
temperature (below Tc, sample is
ferromagnetic)
TN: Néel Temperature (below TN,
sample is antiferromagnetic)
Magnetic Moments
Magnetic moment (μ): relates directly to the number of unpaired electrons
Susceptibility and magnetic moment can be determined experimentally
using a Guoy Balance:
For paramagnetic substance, unpaired
electrons are attracted by the magnetic
field and an apparent increase in mass
of the sample occurs when the field is
switch on
www.geneq.com
Electron Spin Magnetic Moment
Magnetic properties of unpaired electrons arise from electron spin
and electron orbital motion
Bohr magneton (BM): A natural constant which arises in the treatment of
magnetic effects. The magnetic moment is usually
expressed as a multiple of the Bohr magneton.
BM =
eh
4πmc
e: electron charge
h: Planck’s constant
m: electron mass
c: velocity of light
Magnetic moments of
single electron
μs = g√s(s+1)
μs = 1.73 BM
g: gyromagnetic ratio ~2 (for electron
spin magnetic moment)
s: spin quantum number
> 1 unpaired electron
μs = g√S(S+1)
S: sum of spin quantum number
Electron-Orbit Magnetic Moment
The motion of an electron around the nucleus may in some materials,
give rise to an orbital moment, which contributes to the overall
magnetic moment
μS+L = [4S(S+1) + L(L+1)]½
L: orbital angular momentum
quantum number
Simplified approach: a single unpaired electron is set equal to 1 BM
μ = gS
Mechanisms of Magnetic Ordering
The spontaneous alignment of magnetic dipoles in ferro / antiferromagnetic
states need some positive energy of interaction between neighboring spins.
The origin of this coupling is quantum mechanical.
Antiferromagnetism in NiO: superexchange
• The unpaired electrons in these eg orbitals
couple with electrons in the p orbitals of the
O2- ions.
• p orbitals of the O2- ions contain two
electron each, which are coupled
antiparallel.
Origin of Para- and Ferromagnetism in Metals
Pauli Paramagnetism
(paramagnetism of free electrons)
Ferromagnetism
Magnetic Materials-Metal and Alloys
Five transition metals: Cr, Mn, Fe, Co, Ni; and most lanthanides are either
ferro- or antiferromagnetic
Fe, Co, Ni are ferromagnetic; Cr and Mn are antiferromagnetic
How many unpaired electrons are available
to contribute to ferromagnetism:
ferromagnetic
paramagnetic
Tc
Perfect magnetic order is attainable
only at absolute zero
Fact: 2.4 unpaired electron per atom
(in Fe0.8Co0.2 alloy)
Lanthanide Elements
• f-block elements
• f-block unpaired electrons
• They can form both ferro- and antiferromagnetic below room temperature
• Strongest permanent magnet: SmCo5 and Nd2Fe14B
Ferromagnetism
Ferromagnetic materials have domain structure
Hysteresis Loop
Magnetization(M)
Magnetically Hard
Ms
• High Mr and Hc
• Magnetization remains after
the field switch off
(permanent magnet)
Mr
Hc
Applied magnetic field (H)
Magnetically Soft
• Low Mr and Hc (small area)
• Easily demagnetized
Ms: Saturation magnetization
Mr : Remanent magnetization
Hc: Coercive magnetic field
Some More Definitions
1. Magnetocrystalline anisotropy
The energy required to rotate the
magnetization out of the preferred
direction
2. Eddy current
3.
Magnetostriction
The source of energy loss in an
alternating magnetic field
Magnetic materials change their
shape on magnetization
Energy loss:
• The effect increase with H
IV = V2 / R
Eddy currents are minimized in
highly resistive materials.
Metal oxides vs. metals
• Dimensional changes involved are
small, which is comparable to changing
the temperature of the material by a few
degree
Transition Metal Oxides
Monoxides
Dioxides
e.g. NiO
TiO2
Diamagnetic or pauli
paramagnetic
CrO2
ferromagnetic
MnO2
paramagnetic
• d-band (narrow or broad)
• Localized unpaired electrons
• Coupling between d- and sp orbitals
Spinels
Commercially important Ferrites: MFe2O4
M = divalent ion, e.g. Fe2+, Ni2+, Mg2+, Zn2+
•Spinel structure: [Fe3+][M2+,
Fe3+]O4
•Antiferromagnetic or ferrimagnetic
Applications
1. Transformers/motor core
2. Information storage
• Soft magnetic materials
• Soft magnetic materials
• Low hysteresis and eddy current
loss
• unique hysteresis loop
3. Permanent magnet
• Hard magnetic materials
• High curie temperature
• binary digital system